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A Separating Surface for Sitnikov-like n+1-body Problems

We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modelled as a time-dependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle escapes to infinity from those for which it does not. The construction is demonstrated numerically in a few examples

preprint2014arXivOpen access
Lennard BakkerSkyler Simmons
math.DS
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Open access2 authors1 topic
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Lennard BakkerSkyler Simmons

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